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The next two questions refer to the following information: Over the past few decades, public health officials have examined the link between weight concerns and teen girls smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three (63) said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin?

The alternate hypothesis is

  • p < 0 . 30 size 12{p<0 "." "30"} {}
  • p 0 . 30 size 12{p<= 0 "." "30"} {}
  • p 0 . 30 size 12{p>= 0 "." "30"} {}
  • p > 0 . 30 size 12{p>0 "." "30"} {}

D

After conducting the test, your decision and conclusion are

  • Reject H o size 12{H rSub { size 8{o} } } {} : There is sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.
  • Do not reject H o size 12{H rSub { size 8{o} } } {} : There is not sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.
  • Do not reject H o size 12{H rSub { size 8{o} } } {} : There is not sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.
  • Reject H o size 12{H rSub { size 8{o} } } {} : There is sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.

C

The next three questions refer to the following information: A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of attended the midnight showing.

An appropriate alternative hypothesis is

  • p = 0 . 20 size 12{p=0 "." "20"} {}
  • p > 0 . 20 size 12{p>0 "." "20"} {}
  • p < 0 . 20 size 12{p<0 "." "20"} {}
  • p 0 . 20 size 12{p<= 0 "." "20"} {}

C

At a 1% level of significance, an appropriate conclusion is:

  • There is insufficient evidence to conclude that the percent of EVC students that attended the midnight showing of Harry Potter is less than 20%.
  • There is sufficient evidence to conclude that the percent of EVC students that attended the midnight showing of Harry Potter is more than 20%.
  • There is sufficient evidence to conclude that the percent of EVC students that attended the midnight showing of Harry Potter is less than 20%.
  • There is insufficient evidence to conclude that the percent of EVC students that attended the midnight showing of Harry Potter is at least 20%.

A

The Type I error is to conclude that the percent of EVC students who attended is

  • at least 20%, when in fact, it is less than 20%.
  • 20%, when in fact, it is 20%.
  • less than 20%, when in fact, it is at least 20%.
  • less than 20%, when in fact, it is less than 20%.

C

The next two questions refer to the following information:

It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than 7 hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5%, do LTCC Intermediate Algebra students get less than 7 hours of sleep per night, on average?

The distribution to be used for this test is X ~

  • N ( 7 . 24 , 1 . 93 22 ) size 12{N \( 7 "." "24", { { size 8{1 "." "93"} } over { size 8{ sqrt {"22"} } } } \) } {}
  • N ( 7 . 24 , 1 . 93 ) size 12{N \( 7 "." "24",1 "." "93" \) } {}
  • t 22 size 12{t rSub { size 8{"22"} } } {}
  • t 21 size 12{t rSub { size 8{"21"} } } {}

D

The Type II error is to not reject that the mean number of hours of sleep LTCC students get per night is at least 7 when, in fact, the mean number of hours

  • is more than 7 hours.
  • is at most 7 hours.
  • is at least 7 hours.
  • is less than 7 hours.

D

The next three questions refer to the following information: Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen (15) randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test.

The null and alternate hypotheses are:

  • H o : x ¯ = 4 . 5 size 12{H rSub { size 8{o} } : {overline {x}} =4 "." 5} {} , H a : x ¯ > 4 . 5 size 12{H rSub { size 8{a} } : {overline {x}}>4 "." 5} {}
  • H o : μ 4 . 5 size 12{H rSub { size 8{o} } :μ>= 4 "." 5} {} H a : μ < 4 . 5 size 12{H rSub { size 8{a} } :μ<4 "." 5} {}
  • H o : μ = 4 . 75 size 12{H rSub { size 8{o} } :μ=4 "." "75"} {} H a : μ > 4 . 75 size 12{H rSub { size 8{a:} } μ>4 "." "75"} {}
  • H o : μ = 4 . 5 size 12{H rSub { size 8{o} } :μ=4 "." 5} {} H a : μ > 4 . 5 size 12{H rSub { size 8{a} } :μ>4 "." 5} {}

D

At a significance level of a = 0 . 05 size 12{a=0 "." "05"} {} , what is the correct conclusion?

  • There is enough evidence to conclude that the mean number of hours is more than 4.75
  • There is enough evidence to conclude that the mean number of hours is more than 4.5
  • There is not enough evidence to conclude that the mean number of hours is more than 4.5
  • There is not enough evidence to conclude that the mean number of hours is more than 4.75

C

The Type I error is:

  • To conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher.
  • To conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same.
  • To conclude that the mean hours per week currently is 4.5, when in fact, it is higher.
  • To conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher.

B

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Source:  OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
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